trueFLASH: Model-Based Iterative T1 Mapping using Variable-Flip-Angle Fast Low-Angle Shot

Tom Hilbert^{1,2,3}, Damien Nguyen^{4,5}, Jean-Philippe Thiran^{2,3}, Gunnar Krueger^{2,3,6}, Tobias Kober^{1,2,3}, and Oliver Bieri^{4,5}

A 3D standard FLASH sequence was modified in order to perform an undersampling of the k-space using a variable-density Poisson-disc sampling pattern with partial Fourier as exemplarily illustrated in Fig. 1. After obtaining written consent, the prototype sequence was used to acquire 8-fold undersampled FLASH k-spaces with 16 different flip angles (α = 2°,3° … 17°, TA 3:20 min, TR/TE 3.57/1.81ms, resolution 1.3x1.3x1.3mm3, acq. matrix 192x192x128) at 3T (MAGNETOM Prisma, Siemens Healthcare, Germany) using a 20-channels head/neck coil.

As is reported in the literature, the FLASH
signal can be described by the following model^{2},

$$S(T1,K,\alpha)=K\frac{1-\exp(-\frac{TR}{T1})}{1-\cos\alpha\exp(-\frac{TR}{T1})}\sin\alpha$$

with K incorporating various constant effects (e.g.
proton density, coil profile, T2*), TR the repetition time and α the flip angle
(FA). Following Sumpf et al.^{5}, this equation was used as prior
knowledge within a model-based iterative non-linear inversion algorithm in
order to estimate the quantitative maps K and T1 based on the undersampled
data. Additionally, both estimates were spatially regularized using a sparsity
constraint in the wavelet domain.

It should be noted that the nominal FA does not correspond to the real FA in practice due to B1-field inhomogeneities and will lead to corrupted T1 estimates. Therefore, an additional standard B1 map was acquired (TA=2:31min) and used to correct α to be approximately the real FA applied by the sequence.

For validation, the same sequence was applied to acquire a fully sampled k-space with 16 flip angles on a spherical phantom doped with 0.125mM MnCl2 (T1/T2 ~ 870 ms/70 ms). Subsequently, reference T1 values were calculated by fitting the signal model onto the fully sampled data. Additionally, T1 maps were calculated according to DESPOT1 using only two FAs (4° and 15°) and the proposed trueFLASH method with 4 and 8-fold artificial undersampling. The absolute difference to the reference was than calculated in order to visualize the error of each different method.

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^{4}Deoni, Sean CL, Brian
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^{5}Sumpf, Tilman J., et
al. "Model-based nonlinear inverse reconstruction for T2 mapping using
highly undersampled spin-echo MRI." Journal of Magnetic Resonance Imaging
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^{6}Marques, José P., et al. "MP2RAGE, a self
bias-field corrected sequence for improved segmentation and T 1-mapping at high
field." Neuroimage 49.2 (2010): 1271-1281.

^{7}Yarnykh, Vasily L.
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Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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