ArticleMagnetic resonance in medicine2017
Full analytical solution of the bloch equation when using a hyperbolic-secant driving function.
Article in Magnetic resonance in medicine, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 3 papers.
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3 citing papers in PubMed.
- Ultrabroadband 1D and 2D NMR Spectroscopy.Angewandte Chemie (International ed. in English) · 2026Article
- Exact analytical solutions of the Bloch equation for the hyperbolic-secant and chirp pulses.Magnetic resonance in medicine · 2025Article
- In vivo MRI with Concurrent Excitation and Acquisition using Automated Active Analog Cancellation.Scientific reports · 2018Article
Corrections and comments
- Erratum issued
Authors and funding
3 authors.
Funding
Abstract
purposeThe frequency-swept pulse known as the hyperbolic-secant (HS) pulse is popular in NMR for achieving adiabatic spin inversion. The HS pulse has also shown utility for achieving excitation and refocusing in gradient-echo and spin-echo sequences, including new ultrashort echo-time imaging (e.g., Sweep Imaging with Fourier Transform, SWIFT) and B
methodsThe solution of the Bloch-Riccati equation for transverse and longitudinal magnetization for an arbitrary initial state was derived analytically in terms of HS pulse parameters. The analytical solution was compared with the solutions using both the Runge-Kutta method and the small-tip approximation.
resultsThe analytical solution was demonstrated on different initial states at different frequency offsets with/without a combination of HS pulses. Evolution of the transverse magnetization was influenced significantly by the choice of HS pulse parameters. The deviation of the magnitude of the transverse magnetization, as obtained by comparing the small-tip approximation to the analytical solution, was < 5% for flip angles < 30 °, but > 10% for the flip angles > 40 °.
conclusionThe derived analytical solution provides insights into the influence of HS pulse parameters on the magnetization evolution. Magn Reson Med 77:1630-1638, 2017. © 2016 International Society for Magnetic Resonance in Medicine.
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