Slice‐selective extended phase graphs in gradient‐crushed, transient‐state free precession sequences: An application to MR fingerprinting

Abstract

Purpose Slice‐selective, gradient‐crushed, transient‐state sequences such as those used in MR fingerprinting (MRF) relaxometry are sensitive to slice profile effects. Whereas balanced steady‐state free precession MRF profile effects have been studied, less attention has been given to gradient‐crushed MRF forms. Extensions of the extended phase graph (EPG) formalism, called slice‐selective EPG (ssEPG), are proposed that model slice profile effects. Theory and methods The hard‐pulse approximation to slice‐selective excitation in the spatial domain is reformulated in k‐space. Excitation is modeled by standard EPG shift and transition operators. This ssEPG modeling is validated against Bloch simulations and phantom slice profile measurements. ssEPG relaxometry accuracy and variability are compared with other EPG methods in phantoms and human leg in vivo. The role of ∆B0 interactions with slice profile and gradient crushers is investigated. Results Simulations and slice profile measurements show that ssEPG can model highly dynamic slice profile effects of gradient‐crushed sequences. The MRF ssEPG T2 estimates over 0 < T2 < 100 ms improve accuracy by > 10 ms at some values relative to other modeling approaches. Small deviations in B0 can produce substantial bias in T2 estimations from a range of MRF sequence types, and these effects can be modeled and understood by ssEPG. Conclusion Transient‐state, gradient‐crushed sequences such as those used in MRF are sensitive to slice profile effects, and these effects depend on RF pulse choice, gradient crusher strength, and ∆B0. It was found ssEPG was the most accurate EPG‐based means to model these effects.

Fast and accurate modeling of transient‐state, gradient‐spoiled sequences by recurrent neural networks

“…28,37 In conclusion, we combined the best ingredients of both models (Bloch and EPG) into a combined model that is faster than the Bloch simulation and more accurate than the conventional EPG simulator. Recent work 51 process, when signal and derivatives for different sequence parameters need to be computed. Our numerical experiment results show that optimizing a flip-angle train of length 400 for two target tissues requires only 41 s when run on a GPU, and may be further used for accelerating more complicated sequence optimization problems in the future, for example, optimizing sequences for more reconstruction parameters, such as magnetization transfer 52 or B þ 1 .…”

“…The current RNN model learns the signal evolution for a gradient-spoiled sequence with a Gaussian RF excitation pulse. Since RNN architecture is very effective for learning various time-dependent processes, especially those which can be exactly modeled by ordinary differential equations, we believe the proposed RNN model is also able to learn different types of sequences, such as a gradient-spoiled sequence with a different RF shape, RF spoiled sequences or balanced sequences, or different physical models, such as presented in Ostenson et al 51 Retraining for learning new types of sequences or other physical models will be required, but future training can be accelerated by transfer learning approaches 53 in the machine learning field, in which knowledge learned from previous trainings can be applied to a new but related problem. We have not performed experiments on bSSFP sequences yet.…”

A unifying view on extended phase graphs and Bloch simulations for quantitative MRI

“…EPGs are not only numerically stable and computationally efficient, they also provide fundamental insights into MR sequences in terms of dephasing and rephasing configuration pathways, which can interfere and thus modify observed echoes 11 . Extensions to the EPG, such as the spatially-resolved EPG (SR-EPG) 12 – 14 , EPGs with magnetization transfer and exchange (EPG-X) 15 , EPGs with anisotropic diffusion 16 , three-dimensional EPG 17 , or slice-selective EPGs (ssEPG) 18 are examples of the continued efforts to improve signal modelling in conjunction with spoiled sequences.…”

“…This inspired re-evaluation of e.g. transmit field inhomogeneity ( ), diffusion, slice profiles, intra-voxel dephasing, or magnetic field inhomogenieties ( ) in the context of MR Fingerprinting 18 – 25 .…”

“…Moreover, slice profiles have been identified to re-introduce off-resonance dependencies in gradient-spoiled MRF (FISP-MRF). Effective descriptions employing a variant of the SR-EPG have been employed, which resolve the slice profile by independently simulating a full EPG in each position and then summing along the slice dimension (partitioned EPG, pEPG) 13 , 14 , 18 . However, this strategy is only exact in the case of a perfectly homogenous material of infinite or rectangular extent and thus fails to simulate off-resonance artifacts encountered experimentally.…”