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 k_T-points parametrization under explicit power and SAR constraints^3-5.

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 ($$$c_{\hat{s}}$$$):

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

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.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.