S Sivaram Kaushik^{1}, Andrew Huettner^{2}, Peter LaViolette^{3}, Andrew Nencka^{3}, and Kevin Koch^{3}

A nonlinear iterative optimization algorithm was used to design an adiabatic inversion pulse with a bandwidth of 3.2 kHz. With a larger bandwidth, the new pulse maintains the same SAR as the original inversion pulse and also has an improved spectral profile. Images obtained on a phantom, and in-vivo, show improved fat suppression, and reduced ripple artifacts in the slice domain. In addition to improving image quality, the optimized RF pulse may improve the diagnostic ability of STIR with 3D multi spectral imaging.

The original pulse is a 16 ms adiabatic inversion pulse, with a dwell time of 40 μs, a FWHM of 2400 Hz, with a nominal flip angle of 200°, and a peak b1 of 12.18 μT. For the optimization algorithm, a hyperbolic secant pulse with a similar duration and dwell time was chosen as the initial condition. Its RF bandwidth was chosen to be equal to that of the slice selective pulse (3200 Hz). This pulse was Fourier transformed, and 130 Fourier coefficients (65 real, 65 imaginary) were chosen for optimization. These coefficients were tested in a Bloch simulation at 3 RF amplitudes (B1, B1+25%, B1+50%; B1 = 17μT) to test its adiabatic performance. These numbers were used to evaluate a cost function χ

$$$\chi=\sum_0^f(\theta_{B1,A1}-\theta_{Ideal})^{2} + \sum_0^f(\theta_{B1,A2}-\theta_{Ideal})^{2} + \sum_0^f(\theta_{B1,A3}-\theta_{Ideal})^{2} + \lambda_{1}|B_{1,peak}| + \lambda_{2}\sum_0^NB_1^2$$$

where the first 3 terms represent the Bloch simulation evaluation at 3 RF amplitudes, f is the number of points in the spectral domain, N in the time domain. and were empirically determined to be 1000, and 50 respectively. This cost function information was used in a nonlinear optimization routine that updated the Fourier coefficients. Post convergence, the Fourier coefficients were used to generate the time domain RF pulse. The algorithm is summarized in Figure 1.

The performance of the RF pulse was first tested using a prototype MAVRIC SL sequence in a fat-water phantom with a hip implant. The RF pulse was also tested on human volunteers. Written, informed consent was obtained prior to image acquisition, and the study was approved by the local institutional review board.

1) Koch et al., Imaging near metal with a MAVRIC-SEMAC hybrid. Magn Reson Med. 2011;65(1):71-82

2) Lu et al., SEMAC: Slice encoding for metal artifact correction in MRI. Magn Reson Med. 2009;62(1):66-76.

3) Koch et al., Flexible longitudinal magnetization contrast in spectrally overlapped 3D-MSI metal artifact reduction sequences: Technical considerations and clinical impact. Magn. Reson. Med., 74: 1349–1355.

4) Yoon et al., T2-weighted Multispectral Imaging for Postoperative Imaging of Patients with Lumbar Spinal Fusion, In: Proc. Intl. Soc. Mag. Reson. Med. Singapore; 2016:2260.

5) Kaushik et al., Clinically Viable Diffusion-Weighted Imaging Near Metal using 2D-MSI PROPELLER DUO, In: Proc. Intl. Soc. Mag. Reson. Med. Singapore; 2016:370.

6) King et al., Path based phase estimation for fat suppression near metal implants. In: Proc. Intl. Soc. Mag. Reson. Med. Singapore; 2016:3268.

7) Garwood et al., The return of the frequency sweep: designing adiabatic pulses for contemporary NMR. J Magn Reson. 2001;153(2):155-177.

Figure1: Flowchart describing the optimization workflow.

Figure 2: Comparing the
spectral profile of the Gaussian refocusing pulse, original inversion pulse,
and the new optimized inversion pulse. The new inversion pulse has a greater
overlap between the refocusing spectral profile which should greatly diminish
the ripple artifacts.

Figure 3: Phantom results showing improved fat saturation, and fewer
in-plane ripple artifacts. The newer inversion pulse also produces fewer ripple
artifacts in the slice domain.

Figure 4: In vivo results in a
volunteer with an ankle fixation screw. Images C and E show improved fat
saturation with the new pulse and reduced ripple artifacts in the slice domain.

Figure 5: Changing the spectral bin frequency impacts the T1 recovery
of both fat and water resonances. This is seen with the changing contrasts in
the different spectral bins. When combined, this results in a reduced fat
suppression for the 3D-MSI images, which is not a by-product of the RF pulse
used.