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 DESPOT1^3,4. 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.

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,

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

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.

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.