Christian Guenthner^{1}, Sebastian Kozerke^{1}, and Mathieu Sarracanie^{1,2,3}

We propose a multiparametric balanced steady-state 3D Cartesian sequence that exploits model based and pattern matching reconstruction strategies for a series of 20 flip angles and repetition times, allowing for the simultaneous quantification of B_{0}, B_{1}^{+}, T_{1}, T_{2}, and proton density. Time-varying signal patterns at the steady state are reached that allow for the acquisition of unique signal patterns in each image voxel for any acquisition scheme. We show the feasibility of our technique in-vivo in the human brain in 11 minutes, here with Cartesian acquisition and no acceleration strategies.

Our sequence uses a series of 20 different FAs and TRs. Since the sequence parameter space is greatly reduced, optimization of trajectories can be performed to achieve better discrimination of the encoded parameters T_{1}, T_{2}, B_{0}, B_{1}^{+}, and proton density^{2,3}. Discriminatory power of a FA/TR trajectory can be evaluated by calculating the dot product matrix H of a simulated dictionary D^{2,5}:^{ }

H = D†D

The FA and TR train is chosen using stochastic optimization within a predefined set, selecting candidates presenting the minimum averaged correlation coefficient. The optimized sequence presented uses FAs between 10° and 170° and TRs between 11 ms to 41 ms, leading to a total sequence duration of 500 ms per *k-*line. This sequence allows for classical Cartesian acquisition through establishing a stationary steady-state, where the whole sequence is repeated without delay but different imaging gradients^{4}. The pulse sequence diagram of the proposed sequence is shown in Figure 1.

The bSSFP-nature of the presented sequence together with the variation of repetition times lead to high discriminatory power with respect to B_{0} and B_{1}^{+} (correlation < .995), but lower ability to discriminate T_{1} and T_{2} (correlation >.999) (see Figure 2). Thus, in order to correctly resolve T_{1} and T_{2} variations, fine resolution dictionaries for B_{0} and B_{1}^{+} need to be simulated. The dictionary is generated in a two-step process. First, a subspace spanned by B_{0} and B_{1}^{+} is simulated, while T_{1} and T_{2} are fixed. This dictionary is grouped into subgroups using the greedy grouping approach^{6,7}. In a second step, these sub-dictionaries are extended by simulating the respective T_{1} and T_{2} dimensions. In this way, efficient grouping can be realized without the need to perform full-dictionary comparisons.

The sequence was implemented on a 1.5 T Philips Achieva system and data was acquired using an 8-channel head coil. Full head coverage was achieved using non-selective excitation and phase encoding along both phase and slice directions with an elliptical shutter and 1.3-fold slice oversampling. The FOV was 240x225x150 mm^{3}, with an acquisition matrix size of 80x75x25 and 3x3x6 mm^{3} resolution and no parallel imaging (scan duration: 11 min). Reconstruction was performed within 11 minutes using MATLAB on a workstation with twelve cores (2.4 GHz) and a dictionary of 250M entries.

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Figure 1: Sequence diagram of the proposed bSSFP based 3D-non selective Cartesian multiparametric sequence that utilizes a short flip-angle/TR train of 20 without any delays and pre-pulses for rapid quantitative parameter mapping of the brain.

Figure 2: Correlation plots to show discriminatory power of the proposed sequence for B_{0}, B_{1}^{+}, T_{1}, and T_{2} separately. Both, B_{0 }and B_{1}^{+ }show strong variations with correlation values ranging between 0 and 1. T_{1} and T_{2} are both highly correlated. The strong signal variation with regards to B_{0} and B_{1}^{+} can be exploited for highly efficient dictionary grouping by grouping this subdimension first, before the additional T_{1} and T_{2 }dimensions are simulated.

Figure 3: In-vivo 3D Cartesian multiparametric results obtained in the full brain, showing the matching results for three selected slices. T_{1} and T_{2} values are within the expected ranges and grey and white matter can be well separated. Strong static magnetic field gradients at the air-tissue interface close to the ear canals and at the vicinity of the sinuses are visible in the B_{0} maps. Homogeneous off-resonance areas in the skin and cheeks are in accordance with the typical 3.5 ppm chemical shift of water/fat.