Quantitative measurement of relaxation parameters is becoming part of routine clinical scans. To comply with clinical constraints, fast high-resolution T1 mapping techniques are needed. To address this need, techniques such as DESPOT1/T2 [1] and MR Fingerprinting [2] were proposed. Techniques that take advantage of parallel imaging and sparsity have also been proposed. In [3], a Compressed Sensing (CS) based dictionary method for T1 and T2 mapping was introduced. [4] proposed a novel CS based regularization strategy by exploiting signal smoothness along the parametric dimension. Huang et al. proposed model-based methods [5][6] to obtain high-resolution T2 maps from highly undersampled radial fast spin-echo data. In this work, we propose a rapid T1 mapping framework inspired by [5]. The method is based on golden angle radial Inversion-Recovery (IR) steady-state free-precession (SSFP) data acquisition followed by a model-based CS reconstruction that enforces temporal sparsity using a linearized principal components (PCs) model of T1 recovery curves. The proposed method can acquire high resolution T1 maps in less than 3 seconds per slice.

Data are continuously acquired with a SSFP pulse sequence following a 180 degree inversion pulse (Figure 1). The data are divided into groups with N lines/group and the inversion time (TI) of each group is approximated with the average TI of the lines in the group. Since all data are acquired within the recovery time of one inversion pulse, the total imaging time per slice is very short (e.g. <3s). We use a PC-based iterative reconstruction to solve the following problem:

$$\hat{M} = \underset{M}{\text{argmin}} \sum_{j=1}^{TIs} || F_{j}(S(MB_{j}))-K_{j}||_{2}^2+\lambda_{1}TV(M)$$ (1)

In Eq. 1, $$$F_{j}$$$ represents the NUFFT operator for the j^th TI period, $$$S$$$ denotes the coil sensitivity maps, $$$M$$$ represents the PC coefficient maps, $$$B_{j}$$$ is the precomputed truncated PC basis for T1 recovery, $$$K_{j}$$$ is the k-space data at each TI, $$$TV$$$ is the total variation operator on the PC images, $$$\lambda_{1}$$$ is the regularization parameter. Once the PC coefficients are reconstructed, the TI images can be recovered by using $$$I_{j}=\hat{M}B_{j}$$$, which can then be used to generate T1 maps using the method described in [7].

A radial IR-SSFP pulse sequence was implemented on a Siemens 3T Skyra scanner. A phantom consisting of 4 tubes of agar with different concentrations of NiCl₂ was prepared (Table 1). Phantom data were acquired using a 32-element head-and-neck coil with FOV=28cm, matrix size=256x256, TE=1.81ms, TR=3.61ms, TI to the first excitation=54.5ms. An additional experiment to obtain fully-sampled reference data was also carried out. The fully sampled scan consisted of 402 IR-SSFP acquisition units with 256 TRs per unit. The time between IR-SSFP units was 6s. The experiment yielded 256 individual TI images and each TI image was reconstructed from 402 radial views with 256 points per view.

Undersampled and fully sampled in vivo brain data from a normal volunteer were acquired using the same imaging parameters as the phantom. Undersampled abdominal data were acquired using a 32-element body coil with FOV=35cm, matrix size=256x256, TE=1.85ms, TR=3.70ms. As a comparison, an abdominal T1 map was acquired using MOLLI[8] with matrix size of 256x256. We also acquired a higher resolution brain and liver data set with a matrix size of 320x320. This higher resolution setting slightly increased TE and TR, that increased scan time to 2.4s and 2.9s for the abdominal and brain scan respectively. In all our experiments the lines per TI image N was chosen to be 16.

Table 1 compares the T1 values obtained from highly undersampled data (16 lines/TI) to fully sampled data (402 lines/TI). Note that the T1s obtained from highly undersampled data match the T1 values from the fully sampled acquisition. A similar observation can also be made on the brain data (Figure 2). Even at this high rate of acceleration, the spatial details in the brain are well preserved.

Figure 3 shows a T1 map from the proposed method, together with a T1 map from MOLLI [8]. An ROI analysis was performed on to compare average T1 values in the liver. The average T1 values in the ROIs were 860ms and 859ms, for the proposed method and MOLLI, respectively.

Figure 4 shows high-resolution T1 maps for brain and abdominal scans. The brain data has an in-plane resolution=0.78mm and was acquired in 2.9s. The abdominal data has in-plane resolution of 1.0mm and was acquired in 2.4s.

We have proposed a fast T1 mapping method using highly accelerated radial steady-state free-precession sequence and a linearized model-based CS reconstruction. With our proposed method, a high resolution T1 map can be obtained from data acquired in less than 3 seconds.