Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation
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‐dimensiona...
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| Published in | Magnetic resonance in medicine Vol. 59; no. 3; pp. 667 - 672 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken
Wiley Subscription Services, Inc., A Wiley Company
01.03.2008
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0740-3194 1522-2594 1522-2594 |
| DOI | 10.1002/mrm.21542 |
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| 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 = 30 ms, isotropic resolution of 0.95 mm, 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. Magn Reson Med 59:667–672, 2008. © 2008 Wiley‐Liss, Inc. |
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| AbstractList | 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. 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 degrees . 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 degrees and 20 degrees flip angle, TR = 30 ms, isotropic resolution of 0.95 mm, 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. 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 = 30 ms, isotropic resolution of 0.95 mm, 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. Magn Reson Med 59:667–672, 2008. © 2008 Wiley‐Liss, Inc. 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 20DG. 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, 7DG and 20DG flip angle, TR = 30 ms, isotropic resolution of 0.95 mm, 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. 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 = 30 ms, isotropic resolution of 0.95 mm, each 7:09 min). The corresponding estimates of T 1 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 T 1 histograms. Magn Reson Med 59:667–672, 2008. © 2008 Wiley‐Liss, Inc. 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 degrees . 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 degrees and 20 degrees flip angle, TR = 30 ms, isotropic resolution of 0.95 mm, 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.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 degrees . 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 degrees and 20 degrees flip angle, TR = 30 ms, isotropic resolution of 0.95 mm, 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 Dathe, Henning Dechent, Peter |
| Author_xml | – sequence: 1 givenname: Gunther surname: Helms fullname: Helms, Gunther email: ghelms@gwdg.de organization: MR Forschung in der Neurologie und Psychiatrie, Universitätsmedizin, Göttingen, Germany – sequence: 2 givenname: Henning surname: Dathe fullname: Dathe, Henning organization: AG Biomechanik, Abteilung Kieferorthopädie, Universitätsmedizin, Göttingen, Germany – sequence: 3 givenname: Peter surname: Dechent fullname: Dechent, Peter organization: MR Forschung in der Neurologie und Psychiatrie, Universitätsmedizin, Göttingen, Germany |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/18306368$$D View this record in MEDLINE/PubMed |
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| References_xml | – reference: Imran J, Langevin F, Saint-Jalmes H. Two-point method for T1 estimation with optimized gradient-echo acquisition. Magn Reson Imaging 1999; 19: 1347-1256. – reference: Finsterbusch J, Frahm J. Half-Fourier single-shot STEAM MRI. Magn Reson Med 2002; 47: 611-615. – reference: Lu H, Nagae-Poetscher LM, Xavier G, Lin D, Zijl PCMv. Routine clinical brain MRI sequences for use at 3.0 Tesla. J Magn Reson Imaging 2005; 22: 13-22. – reference: Venkatesan R, Lin W, Haacke EM. Accurate determination of spin-density and T1 in the presence of RF-field inhomogeneities and flip-angle miscalibration. Magn Reson Med 1998; 40: 592-602. – reference: Haase A, Frahm J, Matthaei D, Hänicke W, Merboldt K-D. FLASH imaging: rapid NMR imaging using low flip angle pulses. J Magn Reson 1986; 67: 258-266. – reference: Deoni SCL, Peters TM, Rutt BK. High-resolution T1 and T2 mapping of the brain in a clinically acceptable time with DESPOT1 and DESPOT2. Magn Reson Med 2005; 53: 237-241. – reference: Deoni SCL, Rutt BK, Peters TM. Rapid combined T1 and T2 mapping using gradient recalled acquisition in the steady state. Magn Reson Med 2003; 49: 515-526. – reference: Ernst RR, Anderson WA. Application of Fourier transform to magnetic resonance spectroscopy. Rev Sci Instrum 1966; 37: 93-98. – reference: Wang D, Heberlein K, LaConte S, Hu X. Inherent insensitivity to RF inhomogeneity in FLASH imaging. Magn Reson Med 2004; 52: 927-931. – reference: Treier R, Steingoetter A, Fried M, Schwizer W, Boesiger P. Optimized and combined T1 and B1 mapping technique for fast and accurate T1 quantification in contrast-enhanced abdominal MRI. Magn Reson Med 2007; 57: 568-576. – reference: Wang H, Riederer S, Lee S. Optimizing the precision in T1 relaxation estimation using limited flip angles. Magn Reson Med 1986; 5: 399-416. – reference: Whittall K, MacKay A, Graeb D, Nugent R, Li D, Paty D. In vivo measurement of T2 distributions and water contents in normal human brain. Magn Reson Med 1997; 37: 34-43. – reference: Frahm J, Haase A, Matthaei D. Rapid three-dimensional MR imaging using the FLASH technique. J Comput Assist Tomogr 1986; 10: 363-368. – volume: 47 start-page: 611 year: 2002 end-page: 615 article-title: Half‐Fourier single‐shot STEAM MRI publication-title: Magn Reson Med – start-page: 923 year: 2006 – start-page: 1597 year: 2006 – volume: 5 start-page: 399 year: 1986 end-page: 416 article-title: Optimizing the precision in T1 relaxation estimation using limited flip angles publication-title: Magn Reson Med – volume: 40 start-page: 592 year: 1998 end-page: 602 article-title: Accurate determination of spin‐density and T1 in the presence of RF‐field inhomogeneities and flip‐angle miscalibration publication-title: Magn Reson Med – volume: 22 start-page: 13 year: 2005 end-page: 22 article-title: Routine clinical brain MRI sequences for use at 3.0 Tesla publication-title: J Magn Reson Imaging – volume: 53 start-page: 237 year: 2005 end-page: 241 article-title: High‐resolution T1 and T2 mapping of the brain in a clinically acceptable time with DESPOT1 and DESPOT2 publication-title: Magn Reson Med – start-page: 1242 year: 2006 – start-page: 2643 year: 2006 – volume: 49 start-page: 515 year: 2003 end-page: 526 article-title: Rapid combined T1 and T2 mapping using gradient recalled acquisition in the steady state publication-title: Magn Reson Med – volume: 52 start-page: 927 year: 2004 end-page: 931 article-title: Inherent insensitivity to RF inhomogeneity in FLASH imaging publication-title: Magn Reson Med – start-page: 2058 year: 2007 – volume: 37 start-page: 34 year: 1997 end-page: 43 article-title: In vivo measurement of T2 distributions and water contents in normal human brain publication-title: Magn Reson Med – volume: 57 start-page: 568 year: 2007 end-page: 576 article-title: Optimized and combined T1 and B1 mapping technique for fast and accurate T1 quantification in contrast‐enhanced abdominal MRI publication-title: Magn Reson Med – volume: 10 start-page: 363 year: 1986 end-page: 368 article-title: Rapid three‐dimensional MR imaging using the FLASH technique publication-title: J Comput Assist Tomogr – start-page: 1657 year: 2007 – start-page: 111 year: 2003 end-page: 142 – volume: 19 start-page: 1347 year: 1999 end-page: 1256 article-title: Two‐point method for T1 estimation with optimized gradient‐echo acquisition publication-title: Magn Reson Imaging – volume: 67 start-page: 258 year: 1986 end-page: 266 article-title: FLASH imaging: rapid NMR imaging using low flip angle pulses publication-title: J Magn Reson – volume: 37 start-page: 93 year: 1966 end-page: 98 article-title: Application of Fourier transform to magnetic resonance spectroscopy publication-title: Rev Sci Instrum – ident: e_1_2_7_9_2 doi: 10.1002/0470869526.ch5 – ident: e_1_2_7_10_2 – ident: e_1_2_7_16_2 doi: 10.1002/mrm.10090 – ident: e_1_2_7_19_2 – ident: e_1_2_7_8_2 doi: 10.1002/mrm.1910050502 – ident: e_1_2_7_13_2 doi: 10.1002/mrm.1910370107 – ident: e_1_2_7_3_2 doi: 10.1016/S0730-725X(99)00092-2 – ident: e_1_2_7_5_2 doi: 10.1002/mrm.20314 – ident: e_1_2_7_11_2 doi: 10.1063/1.1719961 – ident: e_1_2_7_18_2 – ident: e_1_2_7_20_2 doi: 10.1002/mrm.1910400412 – ident: e_1_2_7_4_2 doi: 10.1002/mrm.10407 – ident: e_1_2_7_6_2 – ident: e_1_2_7_2_2 doi: 10.1016/0022-2364(86)90433-6 – ident: e_1_2_7_12_2 doi: 10.1002/jmri.20356 – ident: e_1_2_7_17_2 – ident: e_1_2_7_21_2 doi: 10.1002/mrm.20217 – ident: e_1_2_7_14_2 doi: 10.1097/00004728-198603000-00046 – ident: e_1_2_7_15_2 – ident: e_1_2_7_7_2 doi: 10.1002/mrm.21177 – reference: - Magn Reson Med. 2010 Apr;63(4):1136 |
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| Snippet | 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... 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... |
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| SubjectTerms | Adult Algorithms Brain Mapping - methods Engineering and Technology Ernst equation Female human brain Humans Imaging, Three-Dimensional Least-Squares Analysis Magnetic Resonance Imaging - methods Male Medical Engineering Medical Imaging Medicinsk bildvetenskap Medicinteknik quantification T1-relaxation Teknik |
| Title | Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation |
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