Bayesian optimization of gradient trajectory for parallel-transmit pulse design

Spoke pulses improve excitation homogeneity in parallel-transmit MRI. We propose an efficient global optimization algorithm, Bayesian optimization of gradient trajectory (BOGAT), for single-slice and simultaneous multislice imaging.

BOGAT adds an outer loop to optimize k_T-space positions. For each position, the RF coefficients are optimized (e.g., with magnitude least squares) and the cost function evaluated. Bayesian optimization progressively estimates the cost function. It automatically chooses the k_T-space positions to sample, to achieve fast convergence, often coming close to the globally optimal spoke positions. We investigated the typical features of spokes cost functions by a grid search with field maps comprising 85 slabs from 14 volunteers. We tested BOGAT in this database, and prospectively in a phantom and in vivo. We compared the vendor-provided Fourier transform approach with the same magnitude least squares RF optimizer.

The cost function is nonconvex and seen empirically to be piecewise smooth with discontinuities where the underlying RF optimum changes sharply. BOGAT converged to within 10% of the global minimum cost within 30 iterations in 93% of slices in our database. BOGAT achieved up to 56% lower flip angle RMS error (RMSE) or 55% lower pulse energy in phantoms versus the Fourier transform approach, and up to 30% lower RMSE and 29% lower energy in vivo with 7.8 s extra computation.

BOGAT efficiently estimated near-global optimum spoke positions for the two-spoke tests, reducing flip-angle RMSE and/or pulse energy in a computation time (˜10 s), which is suitable for online optimization.