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Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation

Helms, Gunther LU orcid ; Dathe, Henning and Dechent, Peter (2008) In Magnetic Resonance in Medicine 59(4). p.667-672
Abstract
From the half-angle substitution of trigonometric terms in the Ernst equation, rational approximations of the flip angle dependence of the FLASH signal can be derived. Even the rational function of the lowest order was in good agreement with the experiment for flip angles up to 20°. Three-dimensional maps of the signal amplitude and longitudinal relaxation rates in human brain were obtained from eight subjects by dual-angle measurements at 3T (nonselective 3D-FLASH, 7° and 20° flip angle, TR=30ms, isotropic resolution of 0.95mm, each 7:09 min). The corresponding estimates of T1 and signal amplitude are simple algebraic expressions and deviated about 1% from the exact solution. They are ill-conditioned to estimate the local flip angle... (More)
From the half-angle substitution of trigonometric terms in the Ernst equation, rational approximations of the flip angle dependence of the FLASH signal can be derived. Even the rational function of the lowest order was in good agreement with the experiment for flip angles up to 20°. Three-dimensional maps of the signal amplitude and longitudinal relaxation rates in human brain were obtained from eight subjects by dual-angle measurements at 3T (nonselective 3D-FLASH, 7° and 20° flip angle, TR=30ms, isotropic resolution of 0.95mm, each 7:09 min). The corresponding estimates of T1 and signal amplitude are simple algebraic expressions and deviated about 1% from the exact solution. They are ill-conditioned to estimate the local flip angle deviation but can be corrected post hoc by division of squared RF maps obtained by independent measurements. Local deviations from the nominal flip angles strongly affected the relaxation estimates and caused considerable blurring of the T1 histograms. (Less)
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Magnetic Resonance in Medicine
volume
59
issue
4
pages
667 - 672
publisher
John Wiley & Sons Inc.
external identifiers
  • scopus:40449133227
ISSN
1522-2594
DOI
10.1002/mrm.21542
project
Algebraization of MRI signal equations
language
English
LU publication?
yes
additional info
3
id
0e73ec4a-b9e7-4828-90ab-3e89a9b6bb28 (old id 8773651)
date added to LUP
2016-04-01 11:50:17
date last changed
2022-04-28 20:44:48
@article{0e73ec4a-b9e7-4828-90ab-3e89a9b6bb28,
  abstract     = {{From the half-angle substitution of trigonometric terms in the Ernst equation, rational approximations of the flip angle dependence of the FLASH signal can be derived. Even the rational function of the lowest order was in good agreement with the experiment for flip angles up to 20°. Three-dimensional maps of the signal amplitude and longitudinal relaxation rates in human brain were obtained from eight subjects by dual-angle measurements at 3T (nonselective 3D-FLASH, 7° and 20° flip angle, TR=30ms, isotropic resolution of 0.95mm, each 7:09 min). The corresponding estimates of T1 and signal amplitude are simple algebraic expressions and deviated about 1% from the exact solution. They are ill-conditioned to estimate the local flip angle deviation but can be corrected post hoc by division of squared RF maps obtained by independent measurements. Local deviations from the nominal flip angles strongly affected the relaxation estimates and caused considerable blurring of the T1 histograms.}},
  author       = {{Helms, Gunther and Dathe, Henning and Dechent, Peter}},
  issn         = {{1522-2594}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{667--672}},
  publisher    = {{John Wiley & Sons Inc.}},
  series       = {{Magnetic Resonance in Medicine}},
  title        = {{Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation}},
  url          = {{http://dx.doi.org/10.1002/mrm.21542}},
  doi          = {{10.1002/mrm.21542}},
  volume       = {{59}},
  year         = {{2008}},
}