Synopsis

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.

Purpose

Balanced Steady-State Free Precession (bSSFP)$$$^1$$$ offers ultra-high resolution structural$$$^{2,3}$$$ and functional$$$^4$$$ imaging at ultra-high field (UHF), but is impaired by $$$B_0$$$-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 $$$B_0$$$-inhomogeneity on bSSFP$$$^{5-9}$$$, and bSSFP can incorporate parallel transmission (PTx) $$$B_1^+$$$-inhomogeneity correction strategies$$$^{3,10}$$$. Here we propose a novel approach to mitigate $$$B_0$$$ and $$$B_1^+$$$-inhomogeneity for bSSFP in a single unified manner. We apply Direct Signal Control$$$^{11,12}$$$ to bSSFP for the first time, harnessing PTx to improve image uniformity in spite of field inhomogeneities.

Methods

The bSSFP steady-state magnetization at TE=TR/2 with flip angle $$$\alpha$$$ and 0-180° phase cycling with relaxation times $$$T_1$$$ and $$$T_2$$$ and off-resonance $$$d\omega$$$ is given below ($$$\mathbf{R}_\beta$$$=rotation matrix of angle $$$\beta$$$, $$$\mathbf{P}_t$$$=precession/$$$T_2$$$-decay matrix for duration $$$t$$$, $$$\mathbf{b}$$$=$$$T_1$$$-recovery vector)$$$^{13}$$$.

$$\mathbf{M}(TR,\alpha,d\omega,T_1,T_2)=\mathbf{P}_{TR/2}[\mathbf{I}-\mathbf{R}_{\alpha}\mathbf{P}_{TR}\mathbf{R}_{-\alpha}\mathbf{P}_{TR}]^{-1}[\mathbf{R}_{\alpha}\mathbf{P}_{TR}\mathbf{R}_{-\alpha}\mathbf{b}+\mathbf{R}_{\alpha}\mathbf{b}]$$

$$$B_0$$$/$$$B_1^+$$$ inhomogeneity results in spatially variable fields (i.e. $$$\alpha=\alpha_j$$$, $$$d\omega=d\omega_j$$$; $$$j$$$=voxel index), causing spatially variable signal $$$f(TR,\alpha_j,d\omega_j,T_1,T_2)=\sqrt{M_x^2+M_y^2}$$$. We propose exploiting additional freedom offered by multiple ($$$N_{tx}$$$) transmitters to achieve signal uniformity by solving the optimization problem below ($$$\Phi$$$=cost function to be minimized, $$$\mathbf{w}$$$=$$$N_{tx}$$$x1 complex vector of RF shims, $$$\alpha_j^k$$$=flip angle profile of transmitter $$$k$$$, $$$i$$$=1,…,$$$N_{tiss}$$$ is an index of included tissues, $$$d_i$$$=desired signal, $$$P_{lim}$$$=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.

Discussion and Conclusions

Acknowledgements

References

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