Improving the time efficiency of the Fourier synthesis method for slice selection in magnetic resonance imaging. Issue 1 (January 2016) - Tahayori, B.; Khaneja, N.; Johnston, L.A.; Farrell, P.M.; Mareels, I.M.Y.
Highlights: Provided novel insight to Fourier synthesis method by representing the Bloch equation in the spherical coordinates. Proposed a novel sequence of pulses to improve the time efficiency of the Fourier synthesis method. Proved the validity of Fourier synthesis method using mathematical induction. Numerically validated the proposed sequence of pulses for slice selection. Introduced a gradient complexity measure to compare the original and the proposed sequence of pulses for slice selection. 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.