Detailed Information

Cited 8 time in webofscience Cited 8 time in scopus
Metadata Downloads

Full Analytical Solution of the Bloch Equation When Using a Hyperbolic-Secant Driving Function

Authors
Zhang, JJ[Zhang, Jinjin]Garwood, M[Garwood, Michael]Park, JY[Park, Jang-Yeon]
Issue Date
Apr-2017
Publisher
WILEY
Keywords
hyperbolic secant; HS pulse; adiabatic pulse; Bloch equation; analytical solution
Citation
MAGNETIC RESONANCE IN MEDICINE, v.77, no.4, pp.1630 - 1638
Indexed
SCIE
SCOPUS
Journal Title
MAGNETIC RESONANCE IN MEDICINE
Volume
77
Number
4
Start Page
1630
End Page
1638
URI
https://scholarworks.bwise.kr/skku/handle/2021.sw.skku/29664
DOI
10.1002/mrm.26252
ISSN
0740-3194
Abstract
Purpose: The frequency-swept pulse known as the hyperbolicsecant (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-1 mapping techniques. To facilitate the analysis of these techniques, the complete theoretical solution of the Bloch equation, as driven by the HS pulse, was derived for an arbitrary state of initial magnetization. Methods: The 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. Results: The 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 degrees, but > 10% for the flip angles > 40 degrees. Conclusion: The derived analytical solution provides insights into the influence of HS pulse parameters on the magnetization evolution. Magn Reson Med 77: 1630-1638, 2017. (C) 2016 International Society for Magnetic Resonance in Medicine
Files in This Item
There are no files associated with this item.
Appears in
Collections
SKKU Institute for Convergence > Biomedical Engineering > 1. Journal Articles

qrcode

Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.

Related Researcher

Researcher PARK, JANG YEON photo

PARK, JANG YEON
Institute for Cross-disciplinary Studies (ICS) (Biomedical Engineering)
Read more

Altmetrics

Total Views & Downloads

BROWSE