Philip K Lee1,2, Lauren E Watkins1,3, Timothy I Anderson2, Guido Buonincontri4,5, Brian A Hargreaves1,2,3. 1. Radiology, Stanford University, Stanford, California. 2. Electrical Engineering, Stanford University, Stanford, California. 3. Bioengineering, Stanford University, Stanford, California. 4. IRCCS Fondazione Stella Maris, Pisa, Italy. 5. Fondazione Imago7, Pisa, Italy.
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 DESPO T 1 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 DESPO T 1 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 N TR = 400 and has O ( N TR ) 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.
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 DESPO T 1 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 DESPO T 1 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 N TR = 400 and has O ( N TR ) 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.
Authors: Eric Van Reeth; Hélène Ratiney; Kevin Tse Ve Koon; Michael Tesch; Denis Grenier; Olivier Beuf; Steffen J Glaser; Dominique Sugny Journal: Magn Reson Med Date: 2018-09-28 Impact factor: 4.668
Authors: Max H C van Riel; Zidan Yu; Shota Hodono; Ding Xia; Hersh Chandarana; Koji Fujimoto; Martijn A Cloos Journal: NMR Biomed Date: 2021-04-26 Impact factor: 4.044