A Near-Resonance Solution to the Bloch Equations and Its Application to RF Pulse Design

A near-resonance expansion of the solution to the Bloch equations in the presence of a radiofrequency (RF) pulse is presented in this paper. The first-order approximation explicitly demonstrates the nonlinear nature of the Bloch equations and precisely relates the excitation profile with the RF pulse when the flip angle is less than π/2. As an application of this solution, we present a procedure for designing RF pulses to generate symmetric excitation profiles with arbitrary shapes for new encoding approaches such as wavelet encoding.