Hyperbolic Secant (HS) pulse has been widely used as an adiabatic inversion pulse for fat suppression in conventional short tau inversion recovery (STIR) sequences, due to its robustness to B1 inhomogeneities. In the areas of increased B0 and B1 inhomogeneities, such as brachial plexus imaging at 3T, the performance of HS pulse suffers due to the tradeoff between adiabatic threshold and bandwidth. The C-shaped frequency offset corrected inversion (C-FOCI) pulse, which is a variant of the HS pulse, has been known for its ability to provide sharper slice profiles^[1,2]. However, the tradeoff between adiabatic threshold and bandwidth of the C-FOCI pulse in the context of fat suppression has not been well established.

The purpose of this work was 1) to establish the tradeoff between adiabatic threshold and bandwidth of the C-FOCI pulse using analytical expressions; and 2) to evaluate the C- FOCI pulse for fat suppression in 3D STIR imaging of the brachial plexus at 3T compared to HS pulse.

C-FOCI pulse is defined as:

$$B_1^{FOCI}=C(t)\times{A_0}sech(\beta{t})\quad\quad(1)\\\triangle\omega^{FOCI}(t) = -C(t)\times{\mu\beta{tanh(\beta{t})}}\quad(2)\\C(t)=\begin{cases}cosh\beta{t}&cosh(\beta{t})<C_{max}\\C_{max}&otherwise\end{cases}\quad(3)$$

where A₀ is the maximum amplitude of B1, β is a modulation angular frequency, μ and C_max are dimensionless parameters. The bandwidth and adiabatic condition of the HS pulse were given by $$$BW_{HS}=2\frac{\mu\beta}{\pi},A_0\gg\frac{\sqrt{\mu}\beta}{\gamma}$$$ respectively^[3]. BW_FOCI, is C_max times larger than that of HS pulse ($$$BW_{FOCI}=C_{max}\times{BW_{HS}}$$$), however, the adiabatic threshold of C-FOCI has not been established analytically before. While the adiabatic threshold of the HS pulse is independent of the off-resonance frequency (Ω) (fig. 1a-1c), it is a function of Ω for C-FOCI pulse. We derived the analytical expression for the adiabatic condition of C-FOCI by solving the adiabatic condition: $$$\gamma\left|\begin{array}{c}\overrightarrow{B_{eff}^\Omega}\end{array}\right|\gg\left|\begin{array}{c}\frac{\partial\psi}{\partial{t}}\end{array}\right|$$$, where $$$\psi$$$ is the angle of the effective B1 with respect to the longitudinal axis.$$A_\Omega\gg\begin{cases}\frac{\sqrt{\mu}\beta}{\gamma}\sqrt{cosh(\beta{t_\Omega})}&|t_\Omega|<\frac{arcosh(C_{max})}{\beta}\\\frac{\sqrt{\mu}\beta}{\sqrt{C_{max}}\times\gamma}& otherwise\end{cases}$$

where $$$t_\Omega$$$ is the time $$$\triangle\omega^{FOCI}(t_\Omega)=\Omega$$$. Subsequently, the analytical solution was verified using Bloch equation simulations and compared against the HS pulses (fig. 1).

The C-FOCI inversion pulse was implemented with 3D STIR on a 3 T Ingenia scanner (Philips Healthcare, Best, The Netherlands). The sequence was first tested on a fat and agarose phantom to compare the fat suppression efficiencies of the C-FOCI and HS pulses by changing B1. The signal intensities of the fat and water were measured and the inversion efficiencies calculated. Subsequently, the 3D STIR with C-FOCI pulse was performed and compared with the default 3D STIR on the brachial plexus of 3 normal volunteers and 2 patients. The scan parameters were: coronal orientation; FOV = 240×380×123 mm; TR/TI = 3000/240 ms; TE = 65 ms; ETL = 130; voxel size = 1.4 ×1.4×1.4 mm, acquired; SENSE acceleration = 2.

The bandwidth of the default HS pulse (HS_4_6) is ~750Hz (fig. 1a) and can be increased by either increasing (HS_4_18) (fig. 1b) or (HS_12_6) (fig. 1c) at the cost of higher adiabatic threshold. Alternatively, the C-FOCI pulse can achieve same bandwidth by increasing C_max without changing μ and β (C-FOCI_4_6_3) (fig. 1d). The analytical calculation of the adiabatic threshold of C-FOCI (eq. 4) matches exactly with the Bloch equation simulations (fig. 1d, dashed red line). The C-FOCI showed lowest adiabatic threshold than the HS pulses with same bandwidth (fig. 1e), confirmed by the phantom experiment (fig. 2). C-FOCI achieved robust fat suppression even at 50% of the maximum B1 (fig. 2b), while the adiabatic threshold of the HS pulse was close to 75% of the maximum B1 (fig. 2g). The calculated inversion efficiencies of water (agarose) and fat matched the simulation results (fig. 3) demonstrating lower adiabatic threshold of 30% for C-FOCI compared to HS at the fat resonance frequency (440 Hz at 3T). Figure 4 shows brachial plexus images of a representative normal volunteer. The B1 map (fig. 4d) shows large B1 inhomogeneities around the neck and left shoulder matching incomplete fat suppression (solid red arrows, fig. 4a) and shading artifacts (dashed red arrow, fig. 4e). Compared to HS pulses, C-FOCI pulse achieved uniform fat suppression. Similarly, the C-FOCI pulse achieved better visualization of the brachial plexus without residual fat and shading artifact compared to default HS in a patient (fig. 5).We have shown the feasibility of C-FOCI pulse as a non-selective adiabatic inversion pulse for robust fat suppression even in the presence of increased B0 and B1 inhomogeneities. Compared to HS pulse, C-FOCI pulse achieves same bandwidth with 30% less sensitivity to B1 variations at fat resonance frequency. We also derived the analytical expression of the adiabatic threshold for C-FOCI pulse, providing a means to determine the optimal tradeoff between the bandwidth and the adiabatic threshold.