trueFLASH: Model-Based Iterative T1 Mapping using Variable-Flip-Angle Fast Low-Angle Shot
Tom Hilbert1,2,3, Damien Nguyen4,5, Jean-Philippe Thiran2,3, Gunnar Krueger2,3,6, Tobias Kober1,2,3, and Oliver Bieri4,5

1Advanced Clinical Imaging Technology (HC CMEA SUI DI BM PI), Siemens Healthcare AG, Lausanne, Switzerland, 2Department of Radiology, University Hospital (CHUV), Lausanne, Switzerland, 3LTS5, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 4Radiological Physics, Department of Radiology, University of Basel Hospital, Basel, Switzerland, 5Department of Biomedical Engineering, University of Basel, Basel, Switzerland, 6Siemens Medical Solutions USA, Inc., Boston, MA, United States


Various methods have been published to quantify the longitudinal relaxation T1; amongst others, a variable-flip-angle fast low-angle shot acquisition can be used. Here, we suggest applying an 8-fold undersampling to such an acquisition, subsequently using a model-based iterative optimization to estimate T1 maps. This approach allows the acquisition of whole-brain 1.3mm isotropic T1 maps within 3:20min using 16 different flip angles. Aliasing artifacts due to the undersampling were successfully removed by the iterative reconstruction. However, the T1 maps show a slight overestimation of T1 values and require a B1-field correction as it is typical for variable-flip-angle approaches.


Longitudinal relaxation T1 proved to be a potential disease biomarker1, and various methods have been published to quantify this tissue parameter2. One approach is to acquire multiple images with variable flip angles (VFA) using a fast low-angle shot (FLASH) sequence. Subsequently, a signal-model is fitted onto the data to estimate T1, a method termed DESPOT13,4. Usually, only a few flip angles (2 to 4) are acquired to avoid long acquisition times. However, this may lead to inaccurate T1 estimation, especially when the data exhibits a low signal-to-noise ratio (SNR). Here, we suggest to undersample the FLASH acquisition and employing the gained acquisition time to acquire more flip angles, resulting in a more robust T1 estimation. We propose to use an iterative model-based optimization, similar to what has been used for quantitative T2 mapping5, to reconstruct the undersampled data.

Materials & Methods

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 model2,


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.

Results & Discussion

Fig. 2 shows the results of the phantom experiments. The trueFLASH 4 and 8-fold acquisitions introduce noise-like errors in the estimation of T1, which can be explained by the incoherent undersampling of k-space. The introduced bias is, however, marginal in comparison to DESPOT1, although acquisition times for DESPOT1 and 8-fold trueFLASH is identical. The estimated T1 within a region of interest (ROI) of the spherical phantom is 0.96+-0.05s, suggesting that the T1 values are slightly overestimated as it is typical for VFA methods especially with short TR7. Fig. 3 shows the quantitative T1 and K maps within two slices of the healthy volunteer. T1 values within regions of interest correspond to what was reported in literature4 with white matter ~0.86 s and grey matter ~1.47 s. However, it should be noted that in some regions the estimation yields rather noisy results, e.g. in the ventricles due to the long T1 of CSF and thus fast FLASH-signal decay. Additionally, the fitted data points are compared to the zero-filled (ZF) and inverse Fourier-transformed data (c.f. Fig. 4 showing three out of 16 FAs). It can be seen that the fitted data resembles the contrast of the ZF data; it exhibits, however, less noise and a higher spatial resolution due to the model-based reconstruction.


We presented an undersampled VFA sequence using a pseudo-random sampling pattern. A model-based iterative optimization is used to reconstruct the undersampled data, intrinsically estimating quantitative T1. This approach allows acquiring a dataset with 16 FAs in the same acquisition time (TA 3:20 min) as it is required for two fully sampled FAs as used in DESPOT1. The increased number of FA directly improves the accuracy of the T1 estimation.


No acknowledgement found.


1Margaret Cheng, Hai-Ling, et al. "Practical medical applications of quantitative MR relaxometry." Journal of Magnetic Resonance Imaging 36.4 (2012): 805-824.

2Stikov, Nikola, et al. "On the accuracy of T1 mapping: searching for common ground." Magnetic Resonance in Medicine 73.2 (2015): 514-522.

3Homer, John, and Martin S. Beevers. "Driven-equilibrium single-pulse observation of T 1 relaxation. A reevaluation of a rapid “new” method for determining NMR spin-lattice relaxation times." Journal of Magnetic Resonance (1969) 63.2 (1985): 287-297.

4Deoni, Sean CL, Brian K. Rutt, and Terry M. Peters. "Rapid combined T1 and T2 mapping using gradient recalled acquisition in the steady state." Magnetic Resonance in Medicine 49.3 (2003): 515-526.

5Sumpf, Tilman J., et al. "Model-based nonlinear inverse reconstruction for T2 mapping using highly undersampled spin-echo MRI." Journal of Magnetic Resonance Imaging 34.2 (2011): 420-428.

6Marques, 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.

7Yarnykh, Vasily L. "Optimal radiofrequency and gradient spoiling for improved accuracy of T1 and B1 measurements using fast steady-state techniques."Magnetic Resonance in Medicine 63.6 (2010): 1610-1626.


Fig. 1: A Poisson-disc sampling pattern combined with partial Fourier. White voxels indicate sampled k-space location and black non-sampled locations.

Fig. 2: T1 maps and their absolute difference to the reference, calculated based on the fully sampled data set with 16 flip angles, fully sampled with only two flip angles (DESPOT1) and the proposed TrueFLASH method with 4-fold and 8-fold acceleration.

Fig. 3: One slice with quantitative maps of a healthy volunteer showing B1 and estimated K and T1 based on an 8-fold accelerated acquisition with 16 variable flip angles.

Fig. 4: The FLASH images acquired with three different flip angles and 8-fold acceleration and reconstructed with a model-based TrueFLASH approach (top) and a zero-filled inverse Fourier transform (bottom).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)