A near-resonance solution to the Bloch equations and its application to RFpulse design

A near-resonance expansion of the solution to the Bloch equations in the pr esence of a radiofrequency (RF) pulse is presented in this paper. The first -order approximation explicitly demonstrates the nonlinear nature of the Bl och equations and precisely relates the excitation profile with the RF puls e when the flip angle is less than pi/2. As an application of this solution , we present a procedure for designing RF pulses to generate symmetric exci tation profiles with arbitrary shapes for new encoding approaches such as w avelet encoding. (C) 1999 Academic Press.