| 1. |
- Dathe, Henning, et al.
(författare)
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Exact algebraization of the signal equation of spoiled gradient echo MRI
- 2010
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Ingår i: Physics in Medicine and Biology. - : IOP Publishing. - 1361-6560 .- 0031-9155. ; 55, s. 4231-4245
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Tidskriftsartikel (refereegranskat)abstract
- The Ernst equation for Fourier transform nuclear magnetic resonance (MR) describes the spoiled steady-state signal created by periodic partial excitation. In MR imaging (MRI), it is commonly applied to spoiled gradient-echo acquisition in the steady state, created by a small flip angle α at a repetition time TR much shorter than the longitudinal relaxation time T1. We describe two parameter transformations of α and TR/T1, which render the Ernst equation as a low-order rational function. Computer algebra can be readily applied for analytically solving protocol optimization, as shown for the dual flip angle experiment. These transformations are based on the half-angle tangent substitution and its hyperbolic analogue. They are monotonic and approach identity for small α and small TR/T1 with a third-order error. Thus, the exact algebraization can be readily applied to fast gradient echo MRI to yield a rational approximation in α and TR/T1. This reveals a fundamental relationship between the square of the flip angle and TR/T1 which characterizes the Ernst angle, constant degree of T1-weighting and the influence of the local radiofrequency field.
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| 2. |
- Helms, Gunther, et al.
(författare)
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High-resolution maps of magnetization transfer with inherent correction for RF inhomogeneity and T1 relaxation obtained from 3D FLASH MRI
- 2008
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 1522-2594 .- 0740-3194. ; 60:6, s. 1396-1407
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Tidskriftsartikel (refereegranskat)abstract
- An empirical equation for the magnetization transfer (MT) FLASH signal is derived by analogy to dual-excitation FLASH, introducing a novel semiquantitative parameter for MT, the percentage saturation imposed by one MT pulse during TR. This parameter is obtained by a linear transformation of the inverse signal, using two reference experiments of proton density and T1 weighting. The influence of sequence parameters on the MT saturation was studied. An 8.5-min protocol for brain imaging at 3T was based on nonselective sagittal 3D-FLASH at 1.25mm isotropic resolution using partial acquisition techniques (TR/TE/flipangle = 25ms/4.9ms/5° or 11ms/4.9ms/15° for the T1 reference). A 12.8 ms Gaussian MT pulse was applied 2.2 kHz off-resonance with 540° flip angle. The MT saturation maps showed an excellent contrast in the brain due to clearly separated distributions for white and gray matter and cerebrospinal fluid. Within the limits of the approximation (excitation <15°, TR/T1<<1) the MT term depends mainly on TR, the energy and offset of the MT pulse, but hardly on excitation and T1 relaxation. It is inherently compensated for inhomogeneities of receive and transmit RF fields. The MT saturation appeared to be a sensitive parameter to depict MS lesions and alterations of normal-appearing white matter.
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| 3. |
- Helms, Gunther, et al.
(författare)
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Identification of signal bias in the variable flip angle method by linear display of the algebraic Ernst equation
- 2011
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 1522-2594 .- 0740-3194. ; 66:3, s. 669-677
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Tidskriftsartikel (refereegranskat)abstract
- A novel linear parameterization for the variable flip angle method for longitudinal relaxation time T1 quantification from spoiled steady state MRI is derived from the half angle tangent transform, t, of the flip angle. Plotting the signal S at coordinates x=St and y=S/t, respectively, establishes a line that renders signal amplitude and relaxation term separately as y-intercept and slope. This representation allows for estimation of the respective parameter from the experimental data. A comprehensive analysis of noise propagation is performed. Numerical results for efficient optimization of longitudinal relaxation time and proton density mapping experiments are derived. Appropriate scaling allows for a linear presentation of data that are acquired at different short pulse repetition times, TR << T1 thus increasing flexibility in the data acquisition by removing the limitation of a single pulse repetition time. Signal bias, like due to slice-selective excitation or imperfect spoiling, can be readily identified by systematic deviations from the linear plot. The method is illustrated and validated by 3T experiments on phantoms and human brain.
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| 4. |
- Helms, Gunther, et al.
(författare)
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Modeling the influence of TR and excitation flip angle on the magnetization transfer ratio (MTR) in human brain obtained from 3D spoiled gradient echo MRI
- 2010
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 1522-2594 .- 0740-3194. ; 64:1, s. 177-185
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Tidskriftsartikel (refereegranskat)abstract
- Attempts to optimize the magnetization transfer ratio (MTR) obtained from spoiled gradient echo MRI have focused on the properties of the magnetization transfer pulse. In particular, continuous-wave models do not explicitly account for the effects of excitation and relaxation on the MTR. In this work, these were modeled by an approximation of free relaxation between the radiofrequency pulses and of an instantaneous saturation event describing the magnetization transfer pulse. An algebraic approximation of the signal equation can be obtained for short pulse repetition time and small flip angles. This greatly facilitated the mathematical treatment and understanding of the MTR. The influence of inhomogeneous radiofrequency fields could be readily incorporated. The model was verified on the human brain in vivo at 3 T by variation of flip angle and pulse repetition time. The corresponding range in MTR was similar to that observed by a 4-fold increase of magnetization transfer pulse power. Choice of short pulse repetition time and larger flip angles improved the MTR contrast and reduced the influence of radiofrequency inhomogeneity. Optimal contrast is obtained around an MTR of 50%, and noise progression is reduced when a high reference signal is obtained.
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| 5. |
- Helms, Gunther, et al.
(författare)
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Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation
- 2008
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Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 1522-2594 .- 0740-3194. ; 59:4, s. 667-672
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Tidskriftsartikel (refereegranskat)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.
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