Flexible and efficient optimization of quantitative sequences using automatic differentiation of Bloch simulations

Abstract

Purpose To investigate a computationally efficient method for optimizing the Cramér‐Rao Lower Bound (CRLB) of quantitative sequences without using approximations or an analytical expression of the signal. Methods Automatic differentiation was applied to Bloch simulations and used to optimize several quantitative sequences without the need for approximations or an analytical expression. The results were validated with in vivo measurements and comparisons to prior art. Multi‐echo spin echo and DESPOT1 were used as benchmarks to verify the CRLB implementation. The CRLB of the Magnetic Resonance Fingerprinting (MRF) sequence, which has a complicated analytical formulation, was also optimized using automatic differentiation. Results The sequence parameters obtained for multi‐echo spin echo and DESPOT1 matched results obtained using conventional methods. In vivo, MRF scans demonstrate that the CRLB optimization obtained with automatic differentiation can improve performance in presence of white noise. For MRF, the CRLB optimization converges in 1.1 CPU hours for NitalicTR = 400 and has O(NTR) asymptotic runtime scaling for the calculation of the CRLB objective and gradient. Conclusions Automatic differentiation can be used to optimize the CRLB of quantitative sequences without using approximations or analytical expressions. For MRF, the runtime is computationally efficient and can be used to investigate confounding factors as well as MRF sequences with a greater number of repetitions.

Rapid three-dimensional multiparametric MRI with quantitative transient-state imaging

“…While here we have used a sequence with a simplified flip angle schedule, various different strategies to optimize the acquisition are possible. For instance, it is possible to optimize the Cramér-Rao Lower Bound of quantitative sequences 9 , 13 , 14 , recently demonstrated also in combination with automatic differentiation algorithms, hence without approximations or an analytical formulation 9 . It is also possible to use Bayesian design theory to define a set of optimal acquisition parameters for a particular range of tissues of interest, maximizing both parameter encoding and experimental efficiency 4 .…”

“…The local quantification accuracy depends both on the used flip angle schedule and the k -space sampling trajectory, as time-dependent point spread functions (PSF) will interfere differently in different spatiotemporal coordinates 7 . So far, the most successful implementations of transient-state imaging have relied on trajectories that oversample the k -space center, such as radial or spiral acquisitions, in combination with locally-smooth schedules of flip angle and repetition times 8 , 9 . Despite their initial success in high-resolution parameter mapping, current quantitative techniques still suffer from limitations in acquisition, reconstruction, and parameter inference efficiency.…”

Retrospective rigid motion correction of three‐dimensional magnetic resonance fingerprinting of the human brain

“…Generally, while T 1 is encoded throughout the schedule after the inversion pulse, T 2 is encoded only by echoes recalled by high FAs; hence, it is harder to estimate and is more susceptible to motion artifacts. Future work including automatic optimization of the schedule might improve also on the motion‐robustness of the technique 43 …”

“…Future work including automatic optimization of the schedule might improve also on the motion-robustness of the technique. 43 Here, we used a gradient-spoiled approach, where subsequent gradients applied in the presence of motion could result in inconsistent dephasing. Therefore, simply co-registering different subsets fails to capture some distortions in the spin-dynamics, in particular when motion occurs in the direction of the spoiling gradient.…”

Magnetic resonance fingerprinting for simultaneous renal T1 and T2* mapping in a single breath‐hold

“…Novel MRF reconstruction methods including deep learning can be used for accelerating the reconstruction and obtain more stable matching progress . Optimizing the pulse sequence by a better choice of the flip angle, TE, and TR may further decrease the noise as published recently …”