A golden angle radial IR-FLASH technique and a principle component based iterative algorithm are developed for high-resolution T1 mapping using highly undersampled 3D radial data. The novel method yields T1 maps of a 3D volume with high spatial and temporal resolution and can cover 144 slices within 5 minutes.
The technique uses a stack-of-stars 3D radial IR-FLASH pulse sequence with golden angle view ordering. As shown in Fig. 1 data for a slab are continuously acquired following a 180o slab-selective inversion pulse. Data acquired after one inversion pulse fills part of the slab’s k-space data needed for T1 mapping, thus, the acquisition is repeated several times (refer here as measurements, M). Figure 2 shows the acquisition order of radial lines. We first collect radial lines at one angle for all kz partitions (as indicated by the blue lines in the figure in M0) and then jump to the next angles (as shown by the orange, purple and red lines) according to an optimized golden angle scheme. After a ~4s collection time, there is a 3s waiting period followed by a second IR-FLASH acquisition to collect radial lines for M1. M measurements are collected to ensure that enough data are acquired for a successful reconstruction.For reconstruction, every P lines collected along kz are considered data for a single TI point, thus N TI points are collected in each measurement, as shown in Fig. 2. The TI time is approximated to the middle TI of this acquisition window. Data from M measurements are combined, ensuring each 3D TI image volume to have M views per partition. To achieve fast imaging each TI data set is highly undersampled (e.g. 3% relative to Nyquist sampling).For T1 mapping an iFFT operation is first used along kz. Since data for each partitions is highly undersampled we use a reconstruction framework based on the inversion-recovery signal model.
$$\hat{T1} = \underset{T1}{\text{argmin}}\sum_{j} ||FT_{j}S_{j} - K_{j}||$$
In Eq. (1) $FT_j$ is the Fourier operator for the jth TI, K_j is the measured k-space data at TIj. S_j is the 3-parameter T1 model proposed in [6], which is a function of T1, TE, TR and flip angle of the excitation RF pulse. The T1 model is linearized using a principal component (PC) basis generated from a set of training curves[5][7-8]. Once the PC coefficients are reconstructed, the TI images are recovered and T1 maps are generated using a method previously described8.Since a slab-selective inversion pulse is used, data from >2 slabs can be acquired in a sequentially by interleaving slabs. This makes the method efficient when high anatomical coverage is needed (e.g. full brain).
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