Signal-domain optimization metrics for MPRAGE RF pulse design in parallel transmission at 7 Tesla
Vincent Gras1, Alexandre Vignaud1, Franck Mauconduit2, Michel Luong3, Alexis Amadon1, Denis Le Bihan1, and Nicolas Boulant1

1Neurospin, CEA/DSV/I2BM, Gif-sur-Yvette, France, 2Siemens Healthcare, Saint-Denis, France, 3IRFU, CEA/DSM, Gif-sur-Yvette, France

### Synopsis

The standard approach to design radiofrequency pulses in MRI is to minimize the deviation of the flip angle from a target value. An alternative approach is proposed here for the MPRAGE sequence which uses the signal as a surrogate of the flip angle in the optimization of the excitation and inversion pulses. The results obtained in simulation and in the brain in vivo on a parallel transmission enabled 7T scanner show two possible applications of the method: an improvement in image quality or a significant reduction of the SAR at equivalent image quality.

### Introduction

Standard radiofrequency (RF) pulse design strategies focus on minimizing the deviation of the flip angle (FA) from a target value. While this approach is sufficient to guarantee the homogeneity of the signal, it may be overconstraining when the MR signal has a nonlinear dependence with the FA. An alternative approach, referred to as the signal-domain optimization, is proposed here for the MPRAGE sequence1 which uses the signal as a surrogate of the FA in the optimization of the excitation and inversion pulses. The concept is presented in the parallel transmission (pTx) framework and exploits the optimization of the kT-points parametrization under explicit power and SAR constraints3-5.

### Methods

In a joint optimization of the excitation and inversion pulses of the MPRAGE sequence, the standard FA homogenizing approach typically consists in minimizing the quantity $U_{\alpha}=\|f_{\alpha}\|_2^2$ where $\|\cdot\|_2$ refers to the voxel-by-voxel summation of the local FA errors using the $\mathcal{L}_2$ norm and where $f_{\alpha}$ is the voxel-wise measure of the FA deviation:

$$f_{\alpha} = \left(1-\frac{\alpha_{\text{Exc}}}{\hat{\alpha}_{\text{Exc}}}\right)^2+\left(1-\frac{\alpha_{\text{Inv}}}{\hat{\alpha}_{\text{Inv}}}\right)^2,$$

$\alpha_{\text{Exc}}$/$\hat{\alpha}_{\text{Exc}}$ and $\alpha_{\text{Inv}}$/$\hat{\alpha}_{\text{Inv}}$ representing the actual/nominal FA for the excitation and inversion pulses respectively. The so-called signal fidelity is now proposed as an alternative to the FA deviation, which relies on the actual, $s(\text{T}_1)$, and nominal, $\hat{s}(\text{T}_1)$, MPRAGE signal2 of the central echo, scaled by $\text{M}_0$. It is defined as:

$$f_s^2 = \frac{\int_I (s-\hat{s})^2 d\text{T}_1}{\int_I \hat{s}^2 d\text{T}_1},$$

where $I$ denotes a $\text{T}_1$ interval covering the values found in brain tissue. A method minimizing $f_s$ may however penalize the local contrast, defined here as the relative signal difference between two voxels exhibiting two different $\text{T}_1$ values, i.e.:

$$c_s(\text{T}_1,\text{T}'_1)=2 \frac{s(\text{T}_1)-s(\text{T}'_1)}{s(\text{T}_1)+s(\text{T}'_1)}.$$

We thus equally define the contrast fidelity as the distance between the actual ($c_s$) and nominal contrast ($c_{\hat{s}}$):

$$f_c^2 = \frac{\iint_{I \times I} (c_s-c_{\hat{s}})^2 d^2\text{T}_1}{\iint_{I \times I} c_{\hat{s}}^2 d^2\text{T}_1},$$

thus vanishing if the actual signal matches the nominal signal up to a multiplicative constant. We now replace the objective $U_{\alpha}$ by the weighted sum of a signal and contrast fidelity terms, to form the new objective function:
$$U_{f,\lambda}=\|F_s\|_2^2+\lambda \|F_c\|_2^2,$$
whereby $F_s$ and $F_c$ are discrete approximations of the continuous integrals $f_s$ and $f_c$ and where $\lambda$ is a weighting factor to be adjusted. The metrics $f_{\alpha}$, $f_s$ and $f_c$ are displayed as functions of $\alpha_{\text{Exc}}$ (x-axis) and $\alpha_{\text{Inv}}$ (y-axis) in Fig. 1 for TR/TI=2.6/1.1s, $\hat{\alpha}_{\text{Exc}}$/$\hat{\alpha}_{\text{Inv}}$ =9/180° and $I = [1,2.3]$ s. Interestingly, the signal domain metrics allow compensating a FA < 180° for the inversion pulse by reducing concomitantly the excitation FA by the proper amount. In Fig. 1.d., the ideal excitation FA is always equal to 9° for $f_{\alpha}$, while for the other metrics, it depends on $\alpha_{\text{Inv}}$. The proposed new optimization metric was thus investigated first in simulation to check if it indeed could return further RF pulse performance or lower the SAR, and was finally tested in vivo with MPRAGE brain acquisitions. Experiments were performed on a Magnetom 7T Siemens scanner (Siemens Healthcare, Erlangen, Germany) equipped with a home-made 8 channel pTx coil and under real-time local SAR supervision6,7.

### Results

L-curve simulations (fidelity versus SAR) revealed that the design of the excitation and inversion pulses with the objective $U_{f,2}$ returned slightly decreased FA homogeneity but higher signal and contrast homogeneity than the FA domain optimization. Alternatively, at equal signal homogeneity, the signal domain optimizations allowed approximately halving the SAR. The obtained MPRAGE brain images are shown in Fig. 2 in four selected regions where sub-plots a-d and a’-d’ correspond to the objectives $U_{\alpha}$ and $U_{f,2}$. A better WM-GM contrast is obtained in Fig. 2.b’ in the cortex while the signal drop in Fig 2.a, caused by a lower excitation FA, is almost suppressed in Fig. 2.a’. Finally, the inhomogeneity in the cerebellum in Fig. 2c or the susceptibility artefacts present in the lateral lobe in Fig. 2.d are significantly reduced in Fig. 2c’ and 2d’. The pulses were designed with explicit 10-g SAR limit of 3 W/kg (the IEC limit being10 W/kg), corresponding to the maximum curvature location of the computed L-curves. This shows that the signal domain optimization also can enable significant SAR reduction while maintaining image quality.

### Conclusions

The proposed RF pulse design optimizes jointly the excitation and inversion pulses of the MPRAGE sequence and exploits the non-linear dependence of the signal with the FAs. The results obtained show two possible applications of the method: an improvement in image quality or a significant reduction of the SAR at equivalent image quality. Although dedicated here to the MPRAGE sequence, this work unveils a possible direction for further improvements in other sequences with marked non-linear signal dependence with FAs.

### Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (FP7/2013-2018) / ERCGrant Agreement n. 309674.

### References

[1] Mugler and Brookeman. MRM 1990;15:152-157. [2] Deichmann et al. NeuroImage 2000;12:112-127. [3] Cloos et al. MRM 2012;67:72–80. [4] Cloos et al. NeuroImage 2012;62:2140-2150. [5] Hoyos-Idrobo et al. IEEE TMI 2014;33:739-748. [6] Eichfelder and Gebhardt. MRM 2011;66:1468-2594. [7] Graesslin et al. MRM 2012;68:1664-1674.

### Figures

Figure 1. Plot of a) the FA deviation, b) the signal and c) contrast fidelity measures and d) the interplay between the excitation and inversion pulses in the minimization of fα, fs or fc.

Figure 2. Comparison of the FA domain (standard approach) and signal domain optimization (proposed approach) in MPRAGE images acquired at 7T.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
4272