Design of adiabatic selective pulses using optimal control theory.

Optimal control theory has been applied in the past for the design of RF pulses for selective excitation. This was the outcome of having established the controllability of the MR spin system for the selective excitation problem. "Minimum distance" was the main formulation used for the solution. Because of their robust behavior in the presence of inhomogeneous RF fields, adiabatic pulses play an important role in spin inversion and excitation. In this study, we present a method for incorporating adiabaticity into the optimal control problem by enhancing the cost functional with an appropriate term. Two different types of adiabatic terms are proposed. Furthermore, two methods are used to solve the optimal control problem, namely the Hamiltonian approach and the solution by mathematical programming. Design examples include both a frequency selective pulse for performing fat suppression by inversion and a regular inversion pulse. It is shown that, in the course of optimization, the pulse designer can trade-off slice resolution against pulse adiabaticity.