Optimal Control Solutions to the Magnetic Resonance Selective Excitation Problem

Most magnetic resonance imaging sequences employ field gradients and amplitude modulated RF pulses to excite only those spins lying in a specific plane. The fidelity of the resulting magnetization distribution is crucial to overall image resolution. Conventional RF-pulse design techniques rely on the small tip-angle approximation to Bloch's equation, which is inadequate for the design of 90 degrees and 180 degrees pulses. This paper demonstrates the existence of a selective pulse, and provides a sound mathematical and computational basis for pulse design. It is shown that the pulses are optimal in the class of piecewise continuous functions of duration T. An optimal pulse is defined as the pulse on the interval that achieves a magnetization profile "closest" to the desired distribution. Optimal control theory provides the mathematical basis for the new pulse design technique. Computer simulations have verified the efficacy of the 90 degrees and the 180 degrees inversion and "pancake-flip" optimal pulses.