We present a method to minimize signal intensity variations observed when performing balanced steady state free precession imaging in non-uniform B0 and B1+ fields. This is achieved by harnessing parallel transmission, with RF shims calculated in order to produce the most uniform signal for the desired tissues given measured B0 and B1+ field maps.
Balanced Steady-State Free Precession (bSSFP)1 offers ultra-high resolution structural2,3 and functional4 imaging at ultra-high field (UHF), but is impaired by B0-inhomogeneity, transmit field (B+1)-inhomogeneity and power deposition. These effects result in SAR-limited UHF-bSSFP acquisitions that produce images with uneven signal/contrast.
Many methods have been developed to mitigate the effects of B0-inhomogeneity on bSSFP5−9, and bSSFP can incorporate parallel transmission (PTx) B+1-inhomogeneity correction strategies3,10. Here we propose a novel approach to mitigate B0 and B+1-inhomogeneity for bSSFP in a single unified manner. We apply Direct Signal Control11,12 to bSSFP for the first time, harnessing PTx to improve image uniformity in spite of field inhomogeneities.
The bSSFP steady-state magnetization at TE=TR/2 with flip angle α and 0-180° phase cycling with relaxation times T1 and T2 and off-resonance dω is given below (Rβ=rotation matrix of angle β, Pt=precession/T2-decay matrix for duration t, b=T1-recovery vector)13.
M(TR,α,dω,T1,T2)=PTR/2[I−RαPTRR−αPTR]−1[RαPTRR−αb+Rαb]
B0/B+1 inhomogeneity results in spatially variable fields (i.e. α=αj, dω=dωj; j=voxel index), causing spatially variable signal f(TR,αj,dωj,T1,T2)=√M2x+M2y. We propose exploiting additional freedom offered by multiple (Ntx) transmitters to achieve signal uniformity by solving the optimization problem below (Φ=cost function to be minimized, w=Ntxx1 complex vector of RF shims, αkj=flip angle profile of transmitter k, i=1,…,Ntiss is an index of included tissues, di=desired signal, Plim=RF power limit used as a surrogate for SAR).
\newcommand{\abs}[1]{\left|#1\right|}\underset{\bf{w}}{\text{minimize}}\enspace\Phi=\sum_{i=1}^{N_{tiss}}\sum_{j=1}^{N_{vox}}\abs{d_i-f\left(TR,\sum_{k=1}^{N_{tx}}\alpha^k_jw^k,d\omega_j,T_1^i,T_2^i\right)}^2\enspace\text{subject}\;\text{to}\enspace\mathbf{w}^*\mathbf{w}\leq\text{P}_{lim}
This approach was tested experimentally. Measurements were performed on a Siemens Magnetom-7T with an eight-channel transmit/receive head coil (Rapid Biomedical). A phantom was constructed containing Magnevist-doped saline (T_1=1236ms, T_2=611ms) with two chambers of 0%-fat milk (T_1=1949ms, T_2=91ms) and a spherical air cavity (diameter=40mm) to induce B_0-inhomogeneity. Images were acquired in a single transverse slice with FOV=200x112.5mm, located 30mm superior to the cavity. Flip angle profiles were obtained by relative B_1^+ mapping^{14,15} and multi-angle absolute B_1^+ mapping^{16}. B_0 shimming utilized a manufacturer-provided protocol (WIP-452G). The center frequency was set to minimize the maximum |d\omega_j|. B_0 mapping was performed with a multi-echo SPGR (TEs=2,4,…,10ms).
Two RF shims were used for bSSFP acquisitions (vox=2x2x1mm, TR=6.7ms, BW=685Hz/pix). The first, \mathbf{w}_{COV}, producing flip angle map \alpha_{COV}, was obtained from a Coefficient-of-Variation (COV) optimisation^{17}, and scaled to achieved an average \alpha=20° (chosen to meet transmitter RF power limits). The second, \mathbf{w}_{OPT}, producing flip angle map \alpha_{OPT}, was obtained from the proposed method. All field information was passed to the routine for calculation, target signals d_i were set as the signals obtained on-resonance with \alpha=20° (i.e. f(TR,20^\circ,0,T_1^i,T_2^i)), and P_{lim}=\mathbf{w}_{COV}^*\mathbf{w}_{COV}. An initial search was performed using 100,00 random RF shims; the 20 best were used for initialisation of the Matlab routine fmincon. \mathbf{w}_{OPT} was chosen as the best solution. The bSSFP acquisitions were corrected for receiver bias to produce I_{COV}^{meas} and I_{OPT}^{meas}, which were compared to the predicted images for each substance and method, I_{COV,i}^{pred} and I_{OPT,i}^{pred}.
Results
The B_0 map (Fig.1b) shows a central perturbation (+55Hz) due to the air cavity. The minimum frequency is -65Hz; note the localized ~10Hz artifact due to the chemical shift of milk. \alpha_{COV} is more uniform than \alpha_{OPT} (Figs.1c/d; standard deviations of 1.9° and 3.8° respectively). Whilst in conventional sequences \alpha_{COV} would produce a more uniform image than \alpha_{OPT}, Fig.2 demonstrates that the converse is true for bSSFP in this scenario.
I_{COV}^{pred} (Fig.2b) has signal hyper/hypo-intensities (black/red arrows) in regions of large B_0-inhomogeneities. These also appear in I_{COV}^{meas} (Fig.2d, blue arrows). I_{OPT}^{pred} shows reduced signal inhomogeneity (Fig.2c, white arrows), which is confirmed by experiment (I_{OPT}^{meas}, Fig.2e, green arrows).
Figure 3 gives further insight. Each image shows the predicted bSSFP signal as a function of d\omega and \alpha (Fig.3a, milk; Fig.3b, saline). The desired signal d_i is indicated in magenta; note that lower \alpha is required to obtain d_i when d\omega≠0. Each overlaid scatter-point corresponds to a voxel (white, I_{COV}^{pred}; black, I_{OPT}^{pred}), placed according to its d\omega_j and corresponding \alpha_j. Signals from I_{COV}^{pred} exhibit less variation along the \alpha-axis as \alpha_{COV} is uniform, but off-resonance distributes the points along the d\omega_j-axis, resulting in non-uniform signal (white arrow). However, our proposed technique alters \alpha_{OPT} so that signals from I_{OPT}^{pred} are closer to the desired signal (red arrow).
Finally, the power ratio \mathbf{w}_{OPT}^*\mathbf{w}_{OPT}/\mathbf{w}_{COV}^*\mathbf{w}_{COV}=0.52; whilst this implies reduced SAR, further experiments are required to see if this is a reproducible feature of the proposed method.
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