Wavelet Domain Radiofrequency Pulse Design Applied to Magnetic Resonance Imaging

Abstract

A new method for designing radiofrequency (RF) pulses with numerical optimization in the wavelet domain is presented. Numerical optimization may yield solutions that might otherwise have not been discovered with analytic techniques alone. Further, processing in the wavelet domain reduces the number of unknowns through compression properties inherent in wavelet transforms, providing a more tractable optimization problem. This algorithm is demonstrated with simultaneous multi-slice (SMS) spin echo refocusing pulses because reduced peak RF power is necessary for SMS diffusion imaging with high acceleration factors. An iterative, nonlinear, constrained numerical minimization algorithm was developed to generate an optimized RF pulse waveform. Wavelet domain coefficients were modulated while iteratively running a Bloch equation simulator to generate the intermediate slice profile of the net magnetization. The algorithm minimizes the L2-norm of the slice profile with additional terms to penalize rejection band ripple and maximize the net transverse magnetization across each slice. Simulations and human brain imaging were used to demonstrate a new RF pulse design that yields an optimized slice profile and reduced peak energy deposition when applied to a multiband single-shot echo planar diffusion acquisition. This method may be used to optimize factors such as magnitude and phase spectral profiles and peak RF pulse power for multiband simultaneous multi-slice (SMS) acquisitions. Wavelet-based RF pulse optimization provides a useful design method to achieve a pulse waveform with beneficial amplitude reduction while preserving appropriate magnetization response for magnetic resonance imaging.

Simultaneous multislice refocusing via time optimal control

“…In total we applied the proposed optimization method to design SMS refocusing pulses with a wide range of MB factors (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) and THK (0.5-2 mm). All optimized pulses show a dramatically reduced pulse duration, on average by 87.1% for the diffusion and by 74.5% for the TSE examples, which allows significant reduction of the minimal TE of both, diffusion and TSE/RARE sequences.…”

“…Historically, the first SMS RF pulse design method is based on a superposition of frequency shifted sub‐pulses . To overcome the limitation of a linear scaling of the B 1 peak amplitude and overall RF power with the MB factor, different groups proposed design methods via phase modulation, time shifted superposition, root‐flipping and use of the wavelet domain . After the pulse design, additional B 1 and power reduction can be achieved by applying variable‐rate selective excitation (VERSE) .…”

“…9 To overcome the limitation of a linear scaling of the B 1 peak amplitude and overall RF power with the MB factor, 4,10 different groups proposed design methods via phase modulation, 11 time shifted superposition, 12 root-flipping 6 and use of the wavelet domain. 13 After the pulse design, additional B 1 and power reduction can be achieved by applying variable-rate selective excitation (VERSE). [14][15][16] However, high MB factors lead to a strong oscillation of the RF amplitude and a direct VERSE application might require additional smoothing of the otherwise too rapidly changing gradient waveform, which was resolved by applying VERSE on the overall RF pulse envelope.…”