General parameter relations for the Shinnar-Le Roux pulse design algorithm

The magnetization ripple amplitudes from a pulse designed by the Shinnar-Le Roux algorithm are a non-linear function of the Shinnar-Le Roux A and B polynomial ripples. In this paper, the method of Pauly et al. [J. Pauly, P. Le Roux, D. Nishimura, A. Macovski, Parameter relations for the Shinnar-Le Roux selective excitation pulse design algorithm, IEEE Transactions on Medical Imaging 10 (1991) 56-65.] has been extended to derive more general parameter relations. These relations can be used for cases outside the five classes considered by Pauly et al., in particular excitation pulses for flip angles that are not small or 90°. Use of the new relations, together with an iterative procedure to obtain polynomials with the specified ripples from the Parks-McClellan algorithm, are shown to give simulated slice profiles that have the desired ripple amplitudes.