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Approximate Fourier domain expression for Bloch–Siegert shift
Author(s) -
Turk Esra Abaci,
Ider Yusuf Ziya,
Ergun Arif Sanli,
Atalar Ergin
Publication year - 2015
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.25104
Subject(s) - expression (computer science) , fourier transform , pulse (music) , frequency domain , envelope (radar) , offset (computer science) , bloch equations , time domain , fourier analysis , physics , resonance (particle physics) , nuclear magnetic resonance , fourier series , phase (matter) , mathematics , mathematical analysis , optics , computer science , atomic physics , quantum mechanics , telecommunications , radar , detector , computer vision , programming language
Purpose In this study, a new simple Fourier domain‐based analytical expression for the Bloch–Siegert (BS) shift‐based B 1 mapping method is proposed to obtain | B 1 + | more accurately while using short BS pulse durations and small off‐resonance frequencies. Theory and Methods A new simple analytical expression for the BS shift is derived by simplifying the Bloch equations. In this expression, the phase is calculated in terms of the Fourier transform of the radiofrequency pulse envelope, and thus making the off‐ and on‐resonance effects more easily understandable. To verify the accuracy of the proposed expression, Bloch simulations and MR experiments are performed for the hard, Fermi, and Shinner–Le Roux pulse shapes. Results Analyses of the BS phase shift‐based B 1 mapping method in terms of radiofrequency pulse shape, pulse duration, and off‐resonance frequency show that | B 1 + | can be obtained more accurately with the aid of this new expression. Conclusions In this study, a new simple frequency domain analytical expression is proposed for the BS shift. Using this expression, | B 1 + | values can be predicted from the phase data using the frequency spectrum of the radiofrequency pulse. This method works well even for short pulse durations and small offset frequencies. Magn Reson Med 73:117–125, 2015. © 2014 Wiley Periodicals, Inc.