title: Improving the time efficiency of the Fourier synthesis method for slice selection in magnetic resonance imaging.
abstract: The design of slice selective pulses for magnetic resonance imaging can be cast as an optimal control problem. The Fourier synthesis method is an existing approach to solve these optimal control problems. In this method the gradient field as well as the excitation field are switched rapidly and their amplitudes are calculated based on a Fourier series expansion. Here, we provide a novel insight into the Fourier synthesis method via representing the Bloch equation in spherical coordinates. Based on the spherical Bloch equation, we propose an alternative sequence of pulses that can be used for slice selection which is more time efficient compared to the original method. Simulation results demonstrate that while the performance of both methods is approximately the same, the required time for the proposed sequence of pulses is half of the original sequence of pulses. Furthermore, the slice selectivity of both sequences of pulses changes with radio frequency field inhomogeneities in a similar way. We also introduce a measure, referred to as gradient complexity, to compare the performance of both sequences of pulses. This measure indicates that for a desired level of uniformity in the excited slice, the gradient complexity for the proposed sequence of pulses is less than the original sequence.
authors.affiliation: Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia. Electronic address: bahmant@unimelb.edu.au.
authors.forename: B
authors.initials: B
authors.lastname: Tahayori
authors.affiliation: School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
authors.forename: N
authors.initials: N
authors.lastname: Khaneja
authors.affiliation: Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia.
authors.forename: L A
authors.initials: LA
authors.lastname: Johnston
authors.affiliation: Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia.
authors.forename: P M
authors.initials: PM
authors.lastname: Farrell
authors.affiliation: Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia.
authors.forename: I M Y
authors.initials: IM
authors.lastname: Mareels
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005583:Fourier Analysis; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008280:Magnetics; D008962:Models, Theoretical; D011846:Radio Waves
keywords: Fourier synthesis; Magnetic resonance imaging; Mathematical induction; Slice selection; The Bloch equation