Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods.

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B(0)) and rf field (B(1)) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.